Gabriela is 16 years younger than Jessica. For the last four years, Jessica and Gabriela have been going to the same school. Five years ago, Jessica was 3 times as old as Gabriela. How old is Jessica now?
Answer: We can use the given information to write down two equations that describe the ages of Jessica and Gabriela. Let Jessica's current age be $j$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $j = g + 16$ Five years ago, Jessica was $j - 5$ years old, and Gabriela was $g - 5$ years old. The information in the second sentence can be expressed in the following equation: $j - 5 = 3(g - 5)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to solve our first equation for $g$ and substitute it into our second equation. Solving our first equation for $g$ , we get: $g = j - 16$ . Substituting this into our second equation, we get the equation: $j - 5 = 3($ $(j - 16)$ $ -$ $ 5)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $j - 5 = 3j - 63$ Solving for $j$ , we get: $2 j = 58$ $j = 29$.